Finite Group Databasebeta

← C139×#13012 #48007608

Subgroups — C139×#13012 #48007608

Order 35584.

590 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D16×C139C211yesmaximal, characteristic
2C2×C4×D8×C139C211yesmaximal, characteristic, complemented
3C2×#357×C139C211yesmaximal, characteristic, complemented
4C2×#357×C139C211yesmaximal, characteristic, complemented
5#1970×C139C211yesmaximal, characteristic, complemented
6#1380×C139C211yesmaximal, characteristic, complemented
7#1374×C139C211yesmaximal, characteristic, complemented
8C22×D8×C139C2211yescharacteristic
9C22×D8×C139C2211yescharacteristic
10C2×C4×D4×C139—21no—
11C2×D16×C139—22no—
12C2×D16×C139—22no—
13C2×D16×C139C414yescomplemented
14C22×C16×C139C2211yescharacteristic
15C22×C16×C139C2211yescharacteristic
16C4×D8×C139—22no—
17C4×D8×C139—22no—
18C2×#107×C139C2211yescharacteristic
19C2×#107×C139C2211yescharacteristic
20C2×#102×C139—21no—
21C2×#102×C139—21no—
22C2×C4×C8×C139C2211yescharacteristic
23#390×C139—21no—
24#357×C139—22no—
25#357×C139—22no—
26C22×D4×C139—21no—
27C22×D4×C139—21no—
28C23×C4×C139—41no—
29C2×D8×C139—21no—
30C2×D8×C139—21no—
31C2×D8×C139—21no—
32C2×D8×C139—21no—
33C2×D8×C139—21no—
34C2×D8×C139—21no—
35C2×D8×C139—21no—
36C2×D8×C139—21no—
37C2×D8×C139C2×C412yes—
38C2×D8×C139C2×C412yescomplemented
39C2×D8×C139D412yes—
40C2×D8×C139D412yes—
41C22×C8×C139D411yescharacteristic
42C22×C8×C139C2311yescharacteristic
43C4×D4×C139—24no—
44C4×D4×C139—42no—
45C2×C4⋊C4×C139—21no—
46C2×C4⋊C4×C139—21no—
47C2×C22⋊C4×C139—41no—
48C2×C22⋊C4×C139—41no—
49C2×C22⋊C4×C139—41no—
50C2×C42×C139D411yescharacteristic
51D16×C139—28no—
52C2×C16×C139—21no—
53C2×C16×C139—21no—
54C2×C16×C139—21no—
55C2×C16×C139—21no—
56C2×C16×C139—21no—
57C2×C16×C139C2×C412yescomplemented
58#107×C139—21no—
59#107×C139—21no—
60#107×C139—21no—
61#107×C139D412yes—
62#102×C139—24no—
63#102×C139—42no—
64C4×C8×C139—21no—
65C4×C8×C139—21no—
66C24×C139—41no—
67C24×C139—41no—
68C2×D4×C139—22no—
69C2×D4×C139—22no—
70C2×D4×C139—22no—
71C2×D4×C139—22no—
72C2×D4×C139—41no—
73C2×D4×C139—41no—
74C2×D4×C139—41no—
75C2×D4×C139—41no—
76C2×D4×C139—41no—
77C2×D4×C139—41no—
78C2×D4×C139—41no—
79C2×D4×C139—41no—
80C22×C4×C139—44no—
81C22×C4×C139—41no—
82C22×C4×C139—41no—
83C22×C4×C139—82no—
84C22×C4×C139—82no—
85C22×C4×C139D811yescharacteristic
86C22×C4×C139D811yescharacteristic
87C22×C4×C139C2×D411yescharacteristic
88D8×C139—22no—
89D8×C139—22no—
90D8×C139—22no—
91D8×C139—22no—
92D8×C139—22no—
93D8×C139—41no—
94D8×C139—41no—
95D8×C139C22⋊C414yescomplemented
96C2×C8×C139—21no—
97C2×C8×C139—21no—
98C2×C8×C139—21no—
99C2×C8×C139C22×C411yescharacteristic
100C2×C8×C139C2×D411yescharacteristic
101C2×C8×C139C2×D411yescharacteristic
102C2×C8×C139C2×D411yescharacteristic
103C2×C8×C139#4111yescharacteristic
104C2×C8×C139#4111yescharacteristic
105C4⋊C4×C139—22no—
106C4⋊C4×C139—41no—
107C4⋊C4×C139—41no—
108C4⋊C4×C139—41no—
109C22⋊C4×C139—44no—
110C22⋊C4×C139—82no—
111C22⋊C4×C139—82no—
112C42×C139—21no—
113C42×C139—21no—
114C16×C139—22no—
115C16×C139—41no—
116C23×C139—42no—
117C23×C139—42no—
118C23×C139—42no—
119C23×C139—42no—
120C23×C139—81no—
121C23×C139—81no—
122C23×C139—81no—
123C23×C139—81no—
124C23×C139—81no—
125C23×C139—81no—
126C23×C139—81no—
127C23×C139—81no—
128C23×C139—81no—
129C23×C139—81no—
130C23×C139C2×D811yescharacteristic
131D4×C139—24no—
132D4×C139—42no—
133D4×C139—42no—
134D4×C139—42no—
135D4×C139—42no—
136D4×C139—42no—
137D4×C139—81no—
138D4×C139—81no—
139C2×C4×C139—21no—
140C2×C4×C139—21no—
141C2×C4×C139—21no—
142C2×C4×C139—21no—
143C2×C4×C139—21no—
144C2×C4×C139—42no—
145C2×C4×C139—88no—
146C2×C4×C139—81no—
147C2×C4×C139—81no—
148C2×C4×C139—81no—
149C2×C4×C139—81no—
150C2×C4×C139—81no—
151C2×C4×C139D1612yescomplemented
152C2×C4×C139C4×D411yescharacteristic
153C2×C4×C139#12011yescharacteristic
154C2×C4×C139#12111yescharacteristic
155C2×C4×C139#13511yescharacteristic
156C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
158C8×C139—41no—
159C8×C139C2×C22⋊C411yescharacteristic
160C8×C139C4×D411yescharacteristic
161C8×C139#12111yescharacteristic
162C8×C139#12311yescharacteristic
163C22×C139—44no—
164C22×C139—82no—
165C22×C139—82no—
166C22×C139—82no—
167C22×C139—82no—
168C22×C139—82no—
169C22×C139—82no—
170C22×C139—82no—
171C22×C139—82no—
172C22×C139—82no—
173C22×C139—161no—
174C22×C139—161no—
175C22×C139—161no—
176C22×C139—161no—
177C22×C139C4×D811yescharacteristic
178C22×C139#44711yescharacteristic
179C22×C139#45911yescharacteristic
180C22×C139C2×D1611yescharacteristic
181C22×C139#50811yescharacteristic
182C22×C139#50911yescharacteristic
183C22×C139#50911yescharacteristic
184C4×C139—22no—
185C4×C139—41no—
186C4×C139—82no—
187C4×C139—161no—
188C4×C139#38611yescharacteristic
189C4×C139#44211yescharacteristic
190C4×C139#44911yescharacteristic
191C4×C139#46311yescharacteristic
192C2×C139—84no—
193C2×C139—162no—
194C2×C139#187911yescharacteristic
195C2×C139C4×D1611yescharacteristic
196C2×C139#217711yescharacteristic
197C2×C139#218411yescharacteristic
198C2×C139#218611yescharacteristic
199C2×C139#220611yescharacteristic
200C2×C139#221011yescharacteristic
201#13012C13911yesmaximal, characteristic, direct product factor, Sylow
202C139#1301211yescharacteristic, direct product factor, Sylow
203C22×D16C2×C13911yescharacteristic
204C2×C4×D8C2×C13911yescharacteristic, complemented
205C2×#357C2×C13911yescharacteristic, complemented
206C2×#357C2×C13911yescharacteristic, complemented
207#1970C2×C13911yescharacteristic, complemented
208#1380C2×C13911yescharacteristic, complemented
209#1374C2×C13911yescharacteristic, complemented
210C22×D8C22×C13911yescharacteristic
211C22×D8C22×C13911yescharacteristic
212C2×C4×D4—21no—
213C2×D16—22no—
214C2×D16—22no—
215C2×D16C4×C13914yescomplemented
216C22×C16C22×C13911yescharacteristic
217C22×C16C22×C13911yescharacteristic
218C4×D8—22no—
219C4×D8—22no—
220C2×#107C22×C13911yescharacteristic
221C2×#107C22×C13911yescharacteristic
222C2×#102—21no—
223C2×#102—21no—
224C2×C4×C8C22×C13911yescharacteristic
225#390—21no—
226#357—22no—
227#357—22no—
228C22×D4—21no—
229C22×D4—21no—
230C23×C4—41no—
231C2×D8—21no—
232C2×D8—21no—
233C2×D8—21no—
234C2×D8—21no—
235C2×D8—21no—
236C2×D8—21no—
237C2×D8—21no—
238C2×D8—21no—
239C2×D8C2×C4×C13912yes—
240C2×D8C2×C4×C13912yescomplemented
241C2×D8D4×C13912yes—
242C2×D8D4×C13912yes—
243C22×C8D4×C13911yescharacteristic
244C22×C8C23×C13911yescharacteristic
245C4×D4—24no—
246C4×D4—42no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C22⋊C4—41no—
250C2×C22⋊C4—41no—
251C2×C22⋊C4—41no—
252C2×C42D4×C13911yescharacteristic
253D16—28no—
254C2×C16—21no—
255C2×C16—21no—
256C2×C16—21no—
257C2×C16—21no—
258C2×C16—21no—
259C2×C16C2×C4×C13912yescomplemented
260#107—21no—
261#107—21no—
262#107—21no—
263#107D4×C13912yes—
264#102—24no—
265#102—42no—
266C4×C8—21no—
267C4×C8—21no—
268C24—41no—
269C24—41no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C22×C4—44no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—82no—
286C22×C4—82no—
287C22×C4D8×C13911yescharacteristic
288C22×C4D8×C13911yescharacteristic
289C22×C4C2×D4×C13911yescharacteristic
290D8—22no—
291D8—22no—
292D8—22no—
293D8—22no—
294D8—22no—
295D8—41no—
296D8—41no—
297D8C22⋊C4×C13914yescomplemented
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8C22×C4×C13911yescharacteristic
302C2×C8C2×D4×C13911yescharacteristic
303C2×C8C2×D4×C13911yescharacteristic
304C2×C8C2×D4×C13911yescharacteristic
305C2×C8#41×C13911yescharacteristic
306C2×C8#41×C13911yescharacteristic
307C4⋊C4—22no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C22⋊C4—44no—
312C22⋊C4—82no—
313C22⋊C4—82no—
314C42—21no—
315C42—21no—
316C16—22no—
317C16—41no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—81no—
323C23—81no—
324C23—81no—
325C23—81no—
326C23—81no—
327C23—81no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23—81no—
332C23C2×D8×C13911yescharacteristic
333D4—24no—
334D4—42no—
335D4—42no—
336D4—42no—
337D4—42no—
338D4—42no—
339D4—81no—
340D4—81no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—88no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4D16×C13912yescomplemented
354C2×C4C4×D4×C13911yescharacteristic
355C2×C4#120×C13911yescharacteristic
356C2×C4#121×C13911yescharacteristic
357C2×C4#135×C13911yescharacteristic
358C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
359C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
360C8—41no—
361C8C2×C22⋊C4×C13911yescharacteristic
362C8C4×D4×C13911yescharacteristic
363C8#121×C13911yescharacteristic
364C8#123×C13911yescharacteristic
365C22—44no—
366C22—82no—
367C22—82no—
368C22—82no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22—82no—
373C22—82no—
374C22—82no—
375C22—161no—
376C22—161no—
377C22—161no—
378C22—161no—
379C22C4×D8×C13911yescharacteristic
380C22#447×C13911yescharacteristic
381C22#459×C13911yescharacteristic
382C22C2×D16×C13911yescharacteristic
383C22#508×C13911yescharacteristic
384C22#509×C13911yescharacteristic
385C22#509×C13911yescharacteristic
386C4—22no—
387C4—41no—
388C4—82no—
389C4—161no—
390C4#386×C13911yescharacteristic
391C4#442×C13911yescharacteristic
392C4#449×C13911yescharacteristic
393C4#463×C13911yescharacteristic
394C2—84no—
395C2—162no—
396C2#1879×C13911yescharacteristic
397C2C4×D16×C13911yescharacteristic
398C2#2177×C13911yescharacteristic
399C2#2184×C13911yescharacteristic
400C2#2186×C13911yescharacteristic
401C2#2206×C13911yescharacteristic
402C2#2210×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C2×D8
commutatorC2×C8C22×C4×C139
Frattini, cosocleC22×C8C23×C139
prime radicalC22×D16×C139C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C42×C139 ◁ C2×C4×C8×C139 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C4×D8×C139C2semidirect
3. C2×#357×C139C2semidirect
4. C2×#357×C139C2semidirect
5. #1970×C139C2semidirect
6. #1380×C139C2semidirect
7. #1374×C139C2semidirect
13. C2×D16×C139C4semidirect
38. C2×D8×C139C2×C4semidirect
57. C2×C16×C139C2×C4semidirect
95. D8×C139C22⋊C4semidirect
151. C2×C4×C139D16semidirect
201. #13012C139direct (N × H)
202. C139#13012direct (N × H)
204. C2×C4×D8C2×C139semidirect
205. C2×#357C2×C139semidirect
206. C2×#357C2×C139semidirect
207. #1970C2×C139semidirect
208. #1380C2×C139semidirect
209. #1374C2×C139semidirect
215. C2×D16C4×C139semidirect
240. C2×D8C2×C4×C139semidirect
259. C2×C16C2×C4×C139semidirect
297. D8C22⋊C4×C139semidirect
353. C2×C4D16×C139semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×D16×C1392
C2×C4×D8×C1392
C2×#357×C1392
#1970×C1392
#1380×C1392
#1374×C1392
#13012139